O R I G I N A L A R T I C L E

C longitudinal relaxation time measurements and DFT-GIAO

NMR computations for two ammonium ions
of a tetraazamacrocyclic scorpiand system

Ryszard B. Nazarski

Received: 28 August 2012 / Accepted: 13 February 2013 / Published online: 2 March 2013
The Author(s) 2013. This article is published with open access at Springerlink.com

Abstract

Spin–lattice relaxation times, T

s, for

nuclei in two cations H

(n = 1, 5) of N-(2-amino-

ethyl)-cyclam (1, scorpiand) were determined by means of

H} NMR experiments in aqueous solution at pH 11.5

and 0.2. The theoretical study [modeling with OPLS-AA,
B3LYP/6-31G(d) geometry optimizations, dispersion-cor-
rected energies (DFT-D3), and DFT-GIAO predictions of
the NMR chemical shifts (including an IEF-PCM simula-
tion of hydration)] was also done for several conformers of
the tautomer iso-H

not investigated before. The bind-

ing directions in protonated polyamino receptors necessary
for efficient complexation of the nitrate anion(s) were
briefly outlined, as well. All these results were discussed in
terms of ‘abnormal’

C chemical shift changes found

previously for the side-chain carbons of amine 1 in strongly
acidic solution (HNO

). In conclusion, an earlier proposal

of its association with NO

at pH\1 was rejected. Instead,

the participation of small amounts of a micro-species
iso-H

hydr

under such conditions can be proposed.

Keywords

‘

Wrong-way’ protonation shift

Amino-

pendant cyclams

NMR pH-titration

Protonated polyamines

Nitrate receptors

Dipolar relaxation

OPLS-AA force field DFT-D3

dispersion correction

Introduction

While NMR chemical shifts d

s (where X = C, H, etc.) and

coupling constants J

belong to the most powerful tools

available for resolution of various structural issues about
organic systems, an increasing interest in the

C spin–lat-

tice (longitudinal) relaxation time T

(hereafter referred to

C SLR and

C T

) is continually observed. Because

such relaxation data vary from milliseconds in macromol-
ecules to several minutes in small objects, the

C-T

value

has become an additional spectral parameter of importance
to the chemist. Indeed, together with nuclear Overhauser
effects arising from

H decoupling of

C NMR spectra, the

values of

C nuclei permit to draw valuable conclusions

about SLR mechanisms operative for individual carbon
atoms in different (bio)organic systems [

–

]. It follows

that they reflect both the inter- and intramolecular mobility
of these entities, and so excellently complement the results
on their dynamics coming from other NMR techniques such
as, e.g., variable-temperature experiments. Hence,

C T

provide a reliable help in the case of some structural
problems very difficult (if at all) to solve by use of more
conventional methods of an NMR spectroscopy.

In our last study on macrocyclic ligands [

the overall

composite conformations of some protonated forms of a
polyamine 1, i.e., 1-(2-aminoethyl)-1,4,8,11-tetraazacyclo-
tetradecane commonly called scorpiand, were proposed on
the basis of its earlier

C NMR pH-titration with nitric

Physical image versus molecular structure relation, Part 16. For Part
15, see Ref. [

Electronic supplementary material

The online version of this

article (doi:

10.1007/s10847-013-0298-x

) contains supplementary

material, which is available to authorized users.

R. B. Nazarski (

Laboratory of Molecular Spectroscopy, Faculty of Chemistry,
University of Ło´dz´, ul. Tamka 12, 91-403 Ło´dz´, Poland
e-mail: nazarski@uni.lodz.pl

A certain erroneous explanation given in Ref. [

] about atoms

C3–C7 and the N

site in two cations H

was corrected in the

Electronic Supplementary Material (p. S7).

123

J Incl Phenom Macrocycl Chem (2014) 78:299–310

DOI 10.1007/s10847-013-0298-x

acid [

]. These spectroscopic data were analyzed in the

light of GIAO (gauge-independent atomic orbitals) [

and

refs therein,

] based predictions of d

s made for numerous

ammonium ions H

coexisting in aqueous media.

Among other issues, we tried to explain an origin of
downfield changes in d

s unexpectedly observed, for atoms

C11 and C12 in the N-pendant-arm unit of amine 1 below
pH *3.5 [

], see Fig. S1 in the Electronic Supplementary

Material; an atom numbering used here is given in the
Formula. As a result, the close proximity of these carbons
to adjacent cationic sites at N

and N

in H

was sug-

gested as one of the possibilities leading to such ‘wrong-
way’ (‘abnormally’ directed) amino-protonation

C NMR

shifts [

]. In fact, an arrangement of the foregoing N atoms

in H

would make possible, in principle, electrostatic

and/or H-bonding-type attractive interactions of these cat-
ionic centers with a single nitrate anion persisting in a close
vicinity of C11/C12. This kind of N

–H_O

–N interac-

tions giving rise to the formation of ion pairs with NO

was reported for

NCH

[

]. After all, it was

finally concluded that the second, ‘structural’ rationaliza-
tion of the observed

C trends is perhaps more reliable.

Indeed, these intriguing

C NMR chemical shift chan-

ges were satisfying reproduced in the time-averaged d

found for GIAO-supported overall shapes of the three
subsequently formed polyammoniums H

(n = 3–5)

[

and refs therein]. The composite conformations of these

macrocyclic ions were found, however, in a non-standard
statistical analysis of the d

sets predicted for their unique

promising forms. In turn, these conformers were chosen
based just on the best agreement of so-computed d

s with

the experimental d

values. But, according to our recent

work [

], large caution must be taken in interpretations of

all

C NMR data-based results on the shapes of molecules

being in dynamic equilibrium between more than two
distinct forms easily feasible energetically. Because it was
also the case of the title ions H

(with non-ionized N

)

[

] and H

existing as ensembles of several fast-

interconverting forms [

], the three explanations of

‘anomalous’ NMR shifts in question should be considered
in details (vide infra).

Thus, it became clear that the additional findings,

both experimental and theoretical, on some protonated
micro-species of the title system 1 were necessary.

Accordingly, two sets of

C-T

times concerning internal

dynamics in its ‘boundary’ ammonium cations H

(n = 1, 5) were determined. In addition, the scarce litera-
ture

C SLR data about pendant-armed tetraaza crowns

–5 were discussed in the light of current findings on these

two ionic scorpiand species. Moreover, several low-energy
conformers of the tautomeric cation iso-H

not ana-

lyzed before were modeled, initially with the OPLS-AA
[

–

] force field and finally at the DFT level, by

applying the equilibrium solvation [

] within an IEF-PCM

approach [

–

]). All these results were taken into

account in a renewed discussion on the origin of ‘abnor-
mal’ NMR trends mentioned above. To the best of our
knowledge, this is the first use of such T

data for structural

analysis of the protonated states of tetraazamacrocycles.
Only the

C-T

based part of this work was presented in a

very preliminary form [

Results and discussion

Possibilities of H-bonding between cations H

(n = 4, 5) and nitrate anion versus ‘wrong-way’
evolutions in NMR chemical shifts

It was obvious that host–guest interactions N

–H_O

–N

typical of H-bond based polyammonium receptors

acting

as hard acids versus NO

as a hard Lewis base could be

ruled out for the macrocyclic amine 1, because of too small
size of its intramolecular hole. Such polyaza hosts (strictly,
their protonated states) showing good selectivity towards
nitrate are 18- to 24-membered aza [

] or oxaza

crowns [

–

]. This monovalent feeble coordinating tri-

gonal oxoanion with poor basicity offers six geometrically
preferred H-bond acceptor sites according to the number
and spatial arrangement of its oxygen’s lone-pair orbitals;
slightly unfavorable H-bonds with the softer p-electrons
are also possible [

and refs therein,

and refs

therein]. In fact, there is an extensive hydration shell
around NO

in water [

and refs therein] as a hard

H-bonding Lewis acid [

]. Hence only specially designed

macrocyclic ionophores encapsulate this anion in the
aforementioned directions, by using the N–H groups in
their binding pockets as strong H-bond donors [

–

]. A

-symmetric environment in the host was found espe-

cially favorable for the NO

binding [

and refs

therein], but this intracavity orientation is not achieved for
the majority of such hosts, mainly due to steric hindrance.
Indeed, any strong receptor-substrate interactions result

For an excellent review in the field of polyammoniums, see e.g.,

Ref. [

300

J Incl Phenom Macrocycl Chem (2014) 78:299–310

123

from the complementary stereoelectronic arrangement of
binding sites in the host and guest [

]. As a result,

only half of the six preferred sites in NO

are usually

occupied and these enable the two specific H-bonding
modes involving all three or only two of its oxygens
[

and refs therein]. Similar molecular-level interactions

were found very recently in the crystal structure of
CH

[

It is also true, that while protonated polyaza macrocycles

with large internal cavities can enfolded [

] or even

encapsulated [

] nitrate(s), most of the single-crystal

X-ray results on such systems showed layered structures with
NO

hovering above and below the mean planes of rela-

tively flat receptors [

–

]. Just such spatial

arrangement was only considered for H

most likely

existing in the pH range 1-4 [

and refs therein], which would

make potentially possible H-bonds with the NO

oxygens.

The fourth protonation of 1 occurring at N

[

] give rise to

the formation of an ‘extended’ all-out conformation of its
macrocyclic unit, which most likely adopts a virtually planar
macroring system, with all exocyclic N

-H bonds in an out

configuration defined by Park and Simmons [

]. An outside

orientation of the ring NH

groups was found for several

polyammoniums of this type [

–

]; see also Figs.

, S3,

and S4. Hence, a relatively rigid H-bond donor system
N

can be considered for H

. But, only its cat-

ionic site at N

would be capable to interact with one discrete

ion, due to unfavorable N

-H bond directions at other

sites. Instead, a dual H-bond donation was likely for two

neighboring cationic centers at N

and N

in H

. So, it was

only possible to think about both these ions (especially, the
latter one) as entities potentially engaged in H-bonds of the
type N–H_O

–N leading to the formation of supermole-

cules [H

][NO

]

and, particularly, [H

][NO

]

as weak

1:1 nitrate associates (ion pairs).

On the other hand, one could discuss about two other

events affecting the protonated states of amine 1, namely,
(i) supporting H-bonding of type C–H_O

–N found in

some crystal structures [

and refs therein] as an equiv-

alent of interactions C–H_O

–X (where X = C or P)

known from NMR pH-titrations of some biomolecules in
aqueous media [

and refs therein]. Its presence

causes ‘wrong-way’ changes in the d

and d

data upon

protonation to a higher and lower magnetic field, respec-
tively. This phenomenon is perhaps electrostatic in origin
and operates through the field. It was recognized as
occurring internally, when a highly negatively charged
group approaches the CH hydrogen(s) [

Moreover, there is the possibility of partial transfer of an

electronic charge from N

to N

of a normal ion n-H

with the formation of its isomeric species iso-H

(Fig.

) as a third (ii) explanation of ‘abnormal’

C NMR

trends in question. Similar ‘wrong-way’ evolution in
chemical shifts is also seen in

N NMR pH-titration of

unsymmetrical linear pentamines, and is explained just by
equilibrium in the protonation of more than one N atom
(charge delocalization) [

The

C relaxation times T

for cations H1

and H

In order to receive a more certain answer to the question
about an origin of the ‘wrong-way’ NMR shifts mentioned
above, two series of SLR times T

C-nuclei in the

14-membered macroring polyamine system 1 were evalu-
ated for its aqueous solution at two pH values (11.5 and
0.2). A dedicated proton-decoupled

C NMR-T

approach

n -H

iso -H

n -H

('reference' tautomer)

Fig. 1

An intramolecular rearrangement possible for the tetraproto-

nated form of amine 1

Table 1

Experimental

C longitudinal relaxation times, T

s, deter-

mined for the atoms C1–C12 in the ions H1

and H

, s

Carbon no.

[pH 11.5]

[pH 0.2]

0.46 (2)

0.29 (2)

0.42 (1

)

0.27 (2)

0.45 (2)

0.42 (2)

0.38 (4)

0.49 (3)

0.29

)

0.40 (1)

0.32 (3)

0.41 (2)

0.30 (2)

0.41 (1)

0.39 (2)

0.36 (4)

0.47 (2)

0.32 (2)

0.49 (4)

0.38

)

0.65 (3)

0.67 (6)

Values given in the parenthesis are ± errors in the last significant

figure

For atom numbering see Fig.

Not determined due to practical overlapping the

C NMR lines

coming from C3 and C8

J Incl Phenom Macrocycl Chem (2014) 78:299–310

301

123

and exponential data analysis were used; see Methods. The
T

s determined in this way for all well-resolved

C lines

originating from 12 or 10 nonequivalent C sites in the
mono- and pentaprotonated form of 1, i.e., ions H1

(with

a protonated atom N

) [

] and H

, respectively, are

listed in Table

. These relaxation data afforded valuable

information on the molecular mobility of both these spe-
cies, which were assumed as two ammonium cations
mainly existing under such conditions. However, some
contribution of the entity H

not fully protonated even

at pH 0.2 can be inferred from the nonzero slope of

NMR pH-titration profiles of 1 in the pH range 0.2–1.0
[

], strongly suggesting not complete protonation. In

fact, an exhaustive protonation can be difficult to
achievement in some cases due to an unfavorable build-up
of positive charges in the macrocycle, especially if its
cavity is small [

]. Such an incomplete ionization was

found for several aza- and oxaza crowns [

–

In any NMR experiment, irradiated nuclei transfer their

excess spin energy to the surrounding in a process of
spin–lattice relaxation (SLR), which rate R

can be

expressed by the sum of pertinent reciprocal relaxation
times T

-1

employing Eq. 1 [

–

¼ 1=T

1;DD

þ 1=T

1;other

ð1Þ

Of the four mechanisms of

C SLR possible for isotropic

solutions of diamagnetic systems with typical (spin I = )
NMR nuclei [dipolar (dipole–dipole, DD), spin-rotation,
chemical-shift anisotropy, and scalar coupling], we can
expect that an intramolecular DD relaxation provides the
dominant effect for pentamine 1 because each of its C
atoms

carries

two

attached

protons.

Indeed,

overwhelming predominance of this mechanism for CH

carbons in structurally close macrocyclic tetramines 2–5
[

] and polyethers [

] was previously found, by

measuring the

C-{

H} Overhauser enhancement factors

obsd

? 1) and calculating the purely DD contributions

to relevant

C T

s, by using Eq. (

) (where g

max

/2c

= 1.988).

1;DD

¼ T

ðg

max

obsd

ð2Þ

For such molecules rapidly reorienting isotropically in a
liquid phase (solution or neat) under

H decoupling and

‘extreme narrowing limit’ conditions, the DD relaxation
rate of the

C nucleus i is very well approximated by Eq.

1=T

1;DD

¼ N

2
C

2
H

c;eff

¼ constant Ns

c;eff

ð3Þ

in which

h is reduced Planck’s constant (:h/2p), c’s are

the gyromagnetic ratios of

C and

H, s

is the molecular

correlation time, r

is an effective C

-H

internuclear

distance (*1.09 A

˚ ), and N is the number of adjacent

protons j, because contributions to

C SLR from the other

protons

are

practically negligible,

due

the

-6

dependence [

–

]. But, such an overall tumbling

cannot easily by resolved into its components (translation,
vibration, rotation) and the average time taken between two
reorientations is defined as an effective correlation time s

The proportionality 1/T

1,DD

is expressed in a rule the

faster a molecule, the longer is T

(and shorter s

), as all

carbons within a given system move at the same rate. Most
of the nonviscous small and medium-sized rigid objects
fulfils this condition. However, conformationally flexible
systems are usually anisotropic in their tumbling and
related s

c,eff

s can be different for each of their C atoms. The

value is then no longer a constant, but inversely

proportional to s

c,eff

(Eq.

)

/ 1=s

c;eff

ð4Þ

and this quantity can be interpreted as an internal mobility
parameter, although only qualitatively and with caution [

Indeed, besides an overall tumbling, the flexible molecules
(such the system 1) may have many modes of internal
mobility, e.g., segmental dynamics along a side arm or
conformational macroring inversions. Each of these
motions modulate the DD interaction between coupled
nuclei.

From the foregoing, it follows that the calculated s

c,eff

data are generally considered as reliable measures of

both the mobility [of the whole molecule (overall tumbling)
and/or its sub-units (segmental mobility)] and the ordering
[

–

]. In our case, all numerical

C T

values found for

two ions H

can be directly compared, because only

groups exist in these species (N = 2). Hence, the

gross consideration of measured SLR data was applied as
completely sufficient for the purpose of our analysis.
Moreover, their overall description exclusively in terms of
a DD mechanism appears appropriate. The same approach
was used in the work [

In contrast to the

C-T

results of Wyrwał et al. [

] on

non-protonated systems of cyclam (3) and its two deriva-
tives 4 and 5, where all macroring backbone carbons can be

(CH

)

(CH

)

2 x = 1, R = CH

3 x = 2, R = H
4 x = 2, R = CO(CH

)

5 x = 2, R = SO

302

J Incl Phenom Macrocycl Chem (2014) 78:299–310

123

treated as dynamically equivalent in CDCl

solution,

analogous atoms in both unsymmetrical ions H

(n = 1

or 5) studied here in water are rather diverse in this respect,
especially in strongly acidic medium. Generally, the
magnitudes of related

C-T

values found for these two

ions are between those reported for azacrowns 3 and 4 [

whereas the shortening of such data for H

relative to

indicates a slower overall tumbling of the former one.

As one can easily see, the mobility of CH

groups in

pendant-arms

and

of these

ions increases with an increasing distance from the mac-
rocycle center (T

s becomes longer, Table

). In both

cases, T

s estimated for a-Cs are equal to the greatest value

found for ring carbons, whereas these parameters for b-Cs
are identical within the error limits (*0.66 s) and, simul-
taneously, they are the longest ones among all of these
relaxation rates. Side-chain segmental motion was apparent
by the lengthening T

s along both aminoalkyl groups

toward their

N terminus. A pronounced degree of

such motion, typical for open-chains, was also reported for
the side arms of 2 and 4 [

]. Indeed, the mean T

values for macroring carbons in two ions H

(of 0.43

and 0.32 s for n = 1 and 5, respectively) can be expected
to approximate the overall T

s of these species. It was

obvious that greater

s found for all four N-pendant-

armed systems mentioned above are due to an added
internal motion, i.e., an enhanced segmental freedom of
their side chains.

The T

value of 0.67 ± 0.06 s, i.e., 2.0 9 *0.32 s

(estimated for the ring), found for C12 in H

is greater

than *0.48 s predicted from simple comparison with
related data for the more mobile H1

(vide supra). How-

ever, this T

(b-C)/T

(ring) % 2.0 is fully consistent with

the analogous T

ratio of 2.25 found in D

O solution for

the

OH unit of 2 [

]. Moreover, our results

indicate much faster internal rotation of the b-CH

group in

at pH 0.2, in agreement with an enhanced mobility

awaited for this site in the

unit solvated by

ion–dipole interactions in strongly polar aqueous solution
[

The conformational flexibility of an internal hole of H1

evaluated in this manner is in good agreement with the
average experimental vicinal interproton coupling

*5.3 Hz. This J-value, typical of rapidly interconverting
cyclic systems, was estimated in a first-order analysis of
ring proton multiplets appeared in the 500 MHz

H NMR

spectrum of 1 recorded at pH 11.5 [

]. On the other hand,

intramolecular H-bonds to adjacent ring nitrogens (or even
being in a dynamic H

-exchange between two such atoms,

NH_H

_HN) [

] are highly probable at this proton-

ation state. Consequently, an internal fluctuation of CH

protons in the macrocyclic backbone of H1

is always

slower than the mobility of such protons in its side-chain.

Similar situation, reflected by comparable magnitudes of

C T

s or substantial line broadening of

H NMR signals,

was also reported for other N-pendant-armed azacrowns
[

In turn, relative small mobility of 1 in its strongly acidic

solution is in line with similar observations made for other
polyhetero macrocycles, which usually are preorganized
structures with specific segmental conformations. To bind
metal cations or protons they may change the shape of each
ring segment, thereby reducing the T

s [

and refs

therein]. A low mobility of H

most likely results from

strong

distance-dependent

Coulombic-type

repulsions

between four positively charged ammonium sites at N

–N

as electrostatic solute ordering effects, which ‘fix’ its
macrocyclic core in a maximally ‘extended’ form adopting
an all-out conformation with ring N-atoms occupying four
corners of the molecular polygon and N

-H bonds directed

toward the outward of an internal cavity (vide supra). An
additional ‘ordering’ can results from interactions between
ring cationic sites and their counter ions or solvent shell of
an aqueous surrounding. All such phenomena have a strong
effect on the s

value [

The aminoalkyl side chain of the monoprotonated base,

, was recognized previously as its highly mobile

fragment. Indeed, the ‘medium’ coupling

*7.1 Hz, a

signature for the fast conformational interconversion [

was estimated at pH 11.5 [

]. In other words, there is a

typical ‘freely’ rotating ethane unit [

]. A practical

equivalence of T

s found for terminal atoms C12 in pen-

dant arms of two discussed ions of 1 indicates that the
analogously fast rotation also occurs around the single
bond CH

-CH

in H

. Obviously, similar mobility

of b-CH

groups in both these species suggests similar

solute–solvent interactions of their outer side chains with
an aqueous environment. For important implications of this
conclusion, see below.

As has already been mentioned, the ‘wrong-way’

NMR pH-titration shifts found for 1 at pH \3.5 were
reproduced quite well by d

s predicted for effective overall

(population-weighted averaged) shapes of the main forms
of cations H

(n = 3–5) coexisting in an acidic medium

[

]. The proposed multicomponent conformations of these

composite shapes called H

ABCD

, n-H

and

ABCD

were, in turn, elucidated by the best fitting

measured d

s to pertinent theoretical d

data computed by

the GIAO B3LYP/6-31G(d) method. Strictly, the NMR
shift of a given C atom, for all of these overall structures,
was obtained as a weighted average d

value of the same

atom in a few preselected forms sampled by a conforma-
tional search at the DFT level. For that reason, the whole
analysis was a little arbitrary, but it was only one approach
possible at this research stage. Nonetheless, in view of the
present

C-T

results on internal dynamics in H1

and

J Incl Phenom Macrocycl Chem (2014) 78:299–310

303

123

, one can accept that an intermolecular H-bond of

type N

–H_O

–N (hypothetically considered before [

in particular for H

) does not operate in aqueous solu-

tion. Without any doubt, such nitrate complexation, giving
rise to the formation of a supermolecule [H

][NO

]

would substantially enforce the rigidity of the pendant-arm
unit in H

. However, the anticipated [

and refs

therein] slowdown of internal dynamics of its two con-
stituent CH

groups rooted by H-bonding mentioned above,

was not found.

The above conclusion is consistent with other consider-

ations. Indeed, a close inspection of low-energy forms of
H

and, especially, H

, which were recognized as

contributing to their composite shapes H

and

ABCD

[

], indicates that ammonium sites in these

protonation states of 1 do not fulfill the highly specific spatial
requirements of the interactions N

–H_O

–N necessary for

efficient complexation of nitrate ion (vide supra). Moreover,
the supporting H-bonds C–H_O

–N are not possible.

Prediction of NMR spectra for the tautomer iso-H

Amines characteristically exhibit small upfield or even
weak downfield protonation shifts for the C atoms a to N
atoms and mostly large high field shifts for b-carbons, in

C NMR spectra [

and refs therein]. During the

protonation of N

as a weakest basis center in pentamine 1,

two b-carbons in the ring, i.e., C2 and C9, show typical
upfield changes at pH\1.5 while side-chain atoms C12 and
especially C11 behave abnormally [

] (Fig. S1). According

to all foregoing facts, a prototropic rearrangement shown in
Fig.

would excellently rationalize these ‘abnormal’ trends

observed. Indeed, deprotonation of some N atoms, at the
expense of protonation of others in close enough proximity
and accompanied by differently directed

C NMR shifts,

was reported for both open-chain [

] and macrocyclic

[

–

] polyamines. Such type ‘wrong-way’ proton-

ation effects in the multinuclear NMR pH-titrations were
sporadically reported for a great variety of small to large
molecules possessing basic sites [

and refs therein].

Thus, several conformers of a tautomeric ion iso-H

not studied to date, with the protonated N

–N

, were gen-

erated applying the OPLS-AA [

–

] force field suc-

cessfully used previously for normal ions n-H

[

]. The

resulting models of iso-H

(Table S1) were refined in

further

quantum–mechanical

DFT-level

calculations,

involving an IEF-PCM hydration simulation, evaluation of
DFT-D3 [

] corrected energies, and GIAO-based predic-

tions of NMR spectra (Methods). Because standard density
functionals do not describe correctly the intramolecular
electron-correlation interactions attributed to van der Waals
dispersion forces [

the adequate DFT-D3 correc-

tions to DFT energies (more precisely, related DG

298.15

data)

were also evaluated for final B3LYP/6-31(d)-optimized
structures; similar approach was used in two recent papers
[

]. All important results found in this way for the

low-energy forms A–D of iso-H

are given in Table S3.

The aforementioned conformers of iso-H

were

recognized as species of higher energy than related forms of
n-H

attained in predominant protonation of atoms

–N

. These forms of iso-H

with an all-out topology

of N–H bonds attached to ring nitrogens were found similar
to those established for H

[

–

]. But, strongly elon-

gated bond C11–N

of *1.585 A

˚ , shorted bond C12–N

(*1.442

˚ ), and slightly flattened amino site at N

were

unexpectedly found for its lowest-energy form A with the
outer unit –CH

in an equatorial position (Fig.

Analogous geometry of the axially oriented side-chain R
was found also for iso-H

(DE

tot

= 2.47 kJ mol

-1

298.15

= 1.81 kJ mol

-1

) and two forms C and D with

and R

, respectively (Table S3). An increase in pyra-

midality at N

on going from A to D, expressed by the sum

of valence angles around this nitrogen,

was also remark-

able. However, all these results on iso-H

were

Fig. 2

PLATON views of two B3LYP/6-31G(d)-optimized lowest

energy ‘hydrated’ forms A (top) and D (bottom) of iso-H

; all N

atoms are shown in blue

For other papers concerning this topic, see e.g., note 45 in Ref. [

Such an approach was used inter alia in Ref. [

304

J Incl Phenom Macrocycl Chem (2014) 78:299–310

123

predicted for a physically unreal case of isolated polyam-
moniums in the gas phase at 0 K, while experimental data
were determined for their strongly polar aqueous solutions
at *294 K. Indeed, various effects of crucial importance
such as interactions with counterions, solvation, thermal
effects, etc. were completely ignored in this standard
approximation ‘of the free-molecule’.

Consequently, simulations of an impact of water mole-

cules on the shape of iso-H

were undertaken, by using

an improved IEF-PCM protocol (Methods). As expected, its
abnormal gas-phase geometry strongly changed after such
‘dissolution’ in water. The resulted forms A

hydr

-D

hydr

, of

iso-H

possess all above bonds of normal length (Table

S3). A large relaxation of their geometry around the
C11–N

bond is noteworthy, in particular.

Obviously, much more important were NMR properties of

such constructed conformers of iso-H

. Thus, four pairs

(iso-H

, n-H

) of the structurally close ions were

considered in order to compute differences in d

s arising

from the change n-H

? iso-H

. All forms A–D of

iso-H

were found as transforming themselves into related

conformers N1 and N2 of n-H

(for their ‘hydrated’ states,

see Figs. S3 and S4) used as ‘reference’ systems with the same
ring geometry, i.e., with protonated N

and unprotonated N

(Table S2). As a result, two narrow intervals Dd

calc

?(13.9–15.5) and -(2.2–3.2) ppm were in vacuo GIAO-
predicted for the atoms C11 and C12, respectively. This trend
was in qualitative agreement with an alteration of ?0.90 and
-0.34 ppm found experimentally for the pH change from
1.02 to 0.24 [

and refs therein]. But, analogous B3LYP/

6-31G(d) IEF-PCM (H

O) NMR predictions on ‘hydrated’

forms A–D, Dd

calc

of ?(6.6–9.8) and -(1.9–3.2) ppm, were in

much better conformity with the experiment, particularly in
the magnitude of the trend (Table S3). An impact of the
geometry relaxation around C11 is evident. In particular, this
concerns the thermodynamically preferred forms A

hydr

and,

especially, D

hydr

with the DFT-D3 corrected DG

298.15

of 1.4

and 0.0 kJ mol

-1

, respectively.

Interestingly, both conformers N1 and N2 of H

were previously recognized as forms most favored in the
gas-phase [

], but they were not proposed finally as

existing in the real aqueous medium on the basis of a
‘solution environment (i.e., NMR spectroscopic) match
criterion’ [

]. Indeed, several forms of some multi-

component systems initially located as their global energy
minima were occasionally not recognized in solutions, by
using typical GIAO-supported approaches [

–

]. The

majority of discrepancies of this kind was usually
explained by specific solute–solvent effects only seldom
adequately taken into account in the computational treat-
ment in normal use. Our recent results on multi-conformer
mixtures [

] and the present findings on H

permit to

be skeptical a bit about the quantitative reliability of

current standard experimental versus computational NMR-
data-based protocols for some flexible systems, especially
those for which only d

s are used in their conformational

analysis. For instance, a presumable uncertainty of such
labor-consuming evaluations of the compositions of equi-
librium mixtures of different forms of H

in aqueous

solution was of the order of 10–15 % [

In view of the foregoing, one can consider the presence of

small amounts of the D

hydr

and A

hydr

forms of iso-H

equilibrated with the N1

hydr

and N2

hydr

forms of n-H

respectively, in the ionic mixture of 1 at pH\1. Indeed, the
full protonation of this pentamine was only arbitrarily
assumed previously (vide supra, see also note 71 in Ref. [

]).

On the other hand, a ‘structural’ rationalization [

] of the

discussed

C trends agreed well with a reasonable postulate

that both atoms C11 and C12 have been in a comparable
chemical environment under used measurement conditions.
The latter assumption resulted, in turn, from large similarity
in the shape of their NMR pH-titration profiles (resemblance
criterion) [

]. A presumable coexistence of some minor

amounts of iso-H

being in dynamic equilibrium with

n-H

is consistent with such conformational landscape.

Generally, the higher energies of localized forms of

iso-H

in relation to those of n-H

seem to be the only

one alarming aspect of a newly proposed explanation of

NMR shifts in question. However, it must be kept in mind
that we meet here with the well-known issue of a doubtful
trustworthiness of today’s computational predictions about
multicharged polyammoniums dissolved in highly polar
aqueous media. Moreover, the presence of NO

as coun-

terions was neglected. Similar relaxation times T

(*0.66 s)

estimated for C12 of 1 at pH 11.5 and 0.2 suggests similarity
in their dynamics and so comparable solute–solvent inter-
actions of its pendant arm in two different surroundings. The
occurrence of the same molecular unit

in H1

and iso-H

would ideally explain practically identical

C-T

values found for their b-CH

groups.

Conclusion

A crucial role of the

C spin–lattice relaxation times

(

C T

s) for elucidating internal molecular dynamics was

presented in the case of two ammonium cations of a
complex tetraazamacrocyclic scorpiand (1) system studied
by this NMR technique in aqueous medium. These exper-
imental T

data, in conjunction with the DFT-level GIAO-

based prediction of

C NMR chemical shifts carried out

for several conformers of the ion iso-H

not studied

before, permitted to suggest the presence of minor amounts
of this tautomer in solution, as a species co-existing in fast
equilibrium with n-H

. Such contribution of iso-H

to the ionic mixture would rationalize, at least in part, an

J Incl Phenom Macrocycl Chem (2014) 78:299–310

305

123

‘abnormal’

C NMR trend found previously for the side-

chain atoms C11/C12 in 1 below pH 1. At the same time,
its earlier working explanation, involving complexation of
a single nitrate anion by the perprotonated form of penta-
mine 1 was rejected in a definitive manner.

Methods

C NMR relaxation measurements

Longitudinal relaxation times, T

s, for

C nuclei in amine 1

(available from an earlier work [

]) were measured at

*294 K on undegassed samples by the inversion-recovery
method [

] on a Varian Gemini 200 BB NMR spec-

trometer operating at 199.98/50.29 MHz (

C). All

experiments were conducted in automation mode under

broad band-decoupling conditions achieved with the
WALTZ-16 sequence [

], by using pulse program of the

software package (version 6.3C) from Varian Associates, Inc.
The (t

-p-s-p/2-t

)

pulse sequence was applied, where t

, s,

and t

were the recycle-delay time, relaxation delay, and

acquisition time, respectively. Twelve different pulse interval
times s between 0.01 and 20 s were used in arrayed experi-
ments, with t

20 s and t

4.2 s. Number of scans, n, was

between 400 and 900, spectral width 3200 Hz, data size 32 K.

High-precision 5-mm NMR sample tubes were used. The

values, originally measured relative to external liquid

tetramethylsilane (TMS) [contained in a coaxially-situated
glass NI5CCI-V insert (with the 2-mm-o.d. stem) delivered
by Norell, Inc. Landisville, NJ, USA], were corrected by a
factor of ?0.72 ppm [

], to account for the difference in

diamagnetic susceptibilities of both liquids involved (Dv

)

[

and refs therein]. Roughly 0.01 mol L

-1

solution of 1 in

O/D

O (*95:5 vol. %) was applied and HNO

was

employed as titrant; the concentration of 1 and D

decreased a little, because of dilution of the sample with the
added acid. Two solutions of pH values about 11.5 and 0.2
were studied; pH-meter readings were not corrected for a
small isotope effect of D

O presents [

]. For details of pH-

metric measurements, see Ref [

]. The T

s for

C nuclei in

the ions H1

and H

were estimated with the aid of two-

parameter non-linear least-squares fitting program provided
by the Varian NMR system. All calculations were carried
out on a spectrometer processor.

Molecular modeling and prediction of NMR spectra

An exhaustive molecular-mechanics (MM) exploration of
the conformational space of iso-H

was performed with

the OPLS-AA [

–

] force field as an energy minimizer,

by using the Monte Carlo (MC)-type GMMX subroutine
of PCMODEL [

]. A randomization [

and refs

therein,

] over various macroring conformers and all

rotatable bonds in the side chain was performed. The
14.6 kJ mol

-1

energy window and dielectric constant (bulk

relative permittivity), e = 78.36 [

], were used in a rough

simulation of hydration.

The returned 25 unique energet-

ically lowest-lying models of iso-H

, embracing the

energy window of 6.2 kJ mol

-1

, were subjected to a gra-

dient gas-phase geometry refinement, initially at HF/3-21G
[

] and then (after some selection) at HF/6-31G(d) and

B3LYP/6-31G(d) levels, by applying the Gaussian 09
program [

] with PCMODEL as its graphical interface.

Seven HF/3-21G promising trial structures A-F of iso-
H

found in this way are listed in Table S1.

In contrast,

all input MM models of the likewise examined ‘reference’
forms N1 and N2 of n-H

were attained departing from

geometries of two structurally close forms of iso-H

, by

their manual deprotonation at N

In addition, frequencies m

were always computed in

harmonic approximation of vibrational modes to verify
whether all localized stationary points represented true
energy minima (NImag = 0) and to determine differences
in standard Gibbs free energies at 298.15 K, DG

298.15

Zero-point energies were evaluated from m

s scaled by a

uniform factor of 0.96 [

]. Finally, Grimme’s DFT-D3

corrections [

] for dispersion-type interactions (London

forces) [

] were applied to so-computed DG

298.15

These correcting terms were calculated with ORCA [

Moreover, simulations of an impact of water molecules on
the shape of ions 1 were performed in an improved equi-
librium solvation protocol [

] of the polarizable contin-

uum model of solvation (IEF-PCM) [

–

], by using UFF

atomic radii. All molecule visualizations were performed
employing PLATON [

–

Single-point in vacuo GIAO [

] B3LYP/6-31G(d)

computations of isotropic magnetic shieldings, r

s, for

components of all four ionic pairs of 1 were carried out at
their B3LYP/6-31G(d) ground-state structures, by using
Gaussian 09. Analogous predictions were also made
applying the foregoing hydration model. The

C NMR

chemical-shift value of a given nucleus in all these entities
was defined as d

calcd

[ppm] = r

stand

- r

calcd

, where r

stand

Calculations were executed for up to 210000 MC steps. A search

was carried out in seven sets of the MM runs, where every series
embraced 30000 MC steps; no new low-energy structure was
generated in the last set.

Two starting MM models of iso-H

, Nos. 22 and 23, with the

bent –CH

unit, underwent rearrangement into forms X and

of n-H

via the 5-membered cyclic transition state (observed on

the monitor screen) with an internal H-bridge of type N_H

_N. A

great degeneration of initial MM models of flexible molecules occurs
occasionally in the geometry refinement at different ab initio levels.
Usually, some changes in relative positions of their energy levels
appear

such

cases,

e.g.,

#1 ? E,

#2 ? F,

#13 ? A,

#14 ? B (Table S1); similar observation was reported in Ref. [

306

J Incl Phenom Macrocycl Chem (2014) 78:299–310

123

was of 189.7155 ppm (in vacuo) or 190.1647 ppm
(IEF-PCM simulations of H

O) as respectively evaluated

for a used NMR reference standard (TMS with the T

symmetry) [

]. All final geometry optimizations, fre-

quency calculations, and GIAO predictions at the DFT
level were done with the keyword Int(Grid = UltraFine).

Acknowledgments

The author thanks Professor Charles L. Perrin

(University of California, San Diego, La Jolla) for very stimulating
correspondence regarding Ref. [

] and ‘wrong-way’ protonation

NMR shifts observed for some polyamino systems, and Dr.
D. Sroczyn´ski (University of Ło´dz´) for pH-metric measurements.
This work was supported in part by calculation facilities and Gaussian
09 software in the Academic Computer Centre CYFRONET (AGH
University of Science and Technology, Krako´w, Poland) through the
computational grant No. MNiSW/SGI3700/UŁo´dzki/057/2010.

Open Access

This article is distributed under the terms of the

Creative Commons Attribution License which permits any use, dis-
tribution, and reproduction in any medium, provided the original
author(s) and the source are credited.

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